Computing the statistical properties of nonlinear random systems is of fundamental importance in many areas of science and engineering. Numerical simulations are always prone to errors that come in many different shapes. In order to understand the relation between realworld systems and numerical simulations, knowledge of error and uncertainty propagation is essential.The primary objective of the course is to introduce students to state-of-the-art methods for uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with systems specified in terms of stochastic ordinary and partial differential equations.